In the starved lubrication regime, the film thickness can be much less than the fully flooded film thickness. The film thickness reduction is related to the inlet meniscus distance. The inlet meniscus and the film thickness can be computed for a given inlet film thickness distribution which is generally non-uniform. The inlet film thickness distribution, which is essentially the outlet film thickness distribution of the previous contact, is affected by the surface tension. In this paper, a modified Coyne-Elrod boundary condition is used to calculate the inlet film thickness distribution, taking the surface tension into account. A numerical analysis of EHL point contacts is carried out and solutions of the inlet meniscus and the film thickness are presented. At lower capillary numbers, side bands formed by reflow in the outlet region can replenish the contact owing to reflow in the inlet region. At higher capillary numbers, the side bands move away from the center of the track and the inlet distance decreases. This is a main cause of starvation in EHL point contacts. A good agreement is found between the numerical solutions and experimental results.